The laws of thermodynamics need to be generalized to the finite, quantum, non-equilibrium
domain. It is by no means clear how to achieve this. In particular, how exactly are we to phrase
the concepts of heat, work and entropy in the most general context ? I plan to review some of the
most relevant approaches and then, based on this, argue that :a) the usual entropies (due to Shannon and von Neumann, classically and quantum respectively)
are not sufficient to discuss state transformations (we need a more general concept of “majorisation”) ;b) the relationship between information and work requires us to use more generalized (Renyi)
entropies ;c) work is, in the quantum setting, not represented by an operator ;d) any conclusions are highly sensitive to how we define the “rules of the game” ;e) how do we include finite time transformations ?

These are just some of the issues we need to face, but there may be others en route to formulating
the most general theory of thermodynamics. This is, of course, not only of pure academic
interest, but is becoming of practical importance though our advances in nano and quantum technologies.
If time permits, I will draw parallels between how we understand entanglement through
local operation and how we formulate thermodynamical entropy.